I'm currently trying to glue some strips of vinyl onto a spandex suit. Yet, nothing I do can keep wrinkles from appearing or any slight movement I do causing it to bunch up. The darn fabric just won't lie flat!

I don't have the option to work with it off my body, so it's me and a friend trying to put it together since I need to be in it since it's stretchy material...But goodness, I'm fixing to lose my mind here.

I don't want to resort to sewing since I'm not that great at it, but I'm really at the edge of my sanity here with this fabric.

You're going to need it to be stretched out somehow before you glue the stuff down (really, sewing would be best), sorry to tell you.
Otherwise it just won't work. You'll put it on and everything will end up in the wrong places, or worse, pop/peel off.